Question

How do you solve `\frac { 3( 6- x ) } { 2} - 3> \frac { 2( 1+ x ) } { 5}`?

Answer 1

`x<56/19`

Explanation:

First, to make life simple, we make sure all three terms have the same denominator. The least common denominator of this equation, as the current denominators are 1, 2, and 5.

`(3(6-x))/2`: We multiply this by `5/5`
`(3(6-x))/2*5/5` = `(5(18-3x))/(2*5)*5/5` = `(90-15x)/(10)`

`-3`: We multiply this by `10/10`
`-3/1*10/10 = -30/10`

`(2(1+x))/5`: We multiply this by `2/2`
`(2(1+x))/5*2/2 = (4(1+x))/(5*2) = (4+4x)/10`

Now, we combine and simplify. The denominators all cancel out through cross multiplication, so we are left with a simple inequality to solve:

`(90-15x)/(10) -30/10 > (4+4x)/10`

=> `(90-15x)-30 > 4+4x`
=> `60-15x > 4+4x`
=> `-19x > -56`
=> `x<56/19`